Alzheimer's disease (AD), as well as normal aging, are associated with a wide range of brain and cognitive changes. In investigating cognitive changes, it has been observed that some people can sustain more brain changes or pathology than others, and this differential susceptibility is related to measures such as IQ, education, vocational experiences etc. This observation is the basis for the cognitive reserve (CR) hypothesis, where CR moderates the effects of brain changes on cognition. Recent developments in medical imaging, particularly multimodal neuroimaging, can provide better understanding of neural mechanisms that underlie both cognitive changes and the role of CR. However, existing statistical methods were not designed to accommodate large-scale multi-dimensional data, particularly for incorporating high-dimensional moderators and mediators. To address these issues, we propose to develop, validate, and apply software tools for the cross-sectional and longitudinal analysis of multimodal MR brain images and cognitive data acquired from individuals with normal cognitive aging, preclinical AD and AD from two independent studies of aging and Alzheimer's disease: the Reference Ability Neural Networks (RANN) (Yaakov Stern, PI) and the Alzheimer's Disease Neuroimaging Initiative (ADNI). We will demonstrate that the developed statistical methods offer improved accuracy and robustness over current tools. First, we will develop tools for identifying robust relationships between neurodegeneration or pathology markers and brain function (network expression measured by task fMRI) in the presence of CR as a moderator. Second, we will derive neural substrate of CR using resting-state functional MRI and task fMRI and then develop statistical tools to test the moderation effect of the imaging CR proxies. Third, we will develop the sparse moderated mediation methods for high-dimensional predictors and mediators accounting for moderation. to test whether network expression during cognitive tasks mediates the effect of brain changes (measured via multimodal structural MRI) on cognitive performance, cognitive decline and dementia transition, and whether the derived neural substrate of CR moderates the mediation.